1. Field of application of the invention
The invention relates to an arrangement for computing Fourier coefficients C.sub.n of a real input signal, which input signal corresponds with a time sequence of N time- and amplitude discrete samples X.sub.k, which device is provided with a pre-processing device to which N discrete samples X.sub.k are applied through an input circuit which is provided with a storage device having at least two outputs; a first multiplying device for multiplying complex numbers, which is connected to the outputs of said storage device and a complex number generator; a FET computer unit which is connected to said multiplying device.
Such an arrangement is applicable to spectral analyses or to filtering of signals.
2. Description of the prior art
The techniques for computing the discrete Fourier transform of a series of equidistant samples of a signal has already been the subject of many publications. See, for example, reference 1 of section (D) below. The most effective manner for computing the discrete Fourier Transform (DFT) is known as "Fast Fourier Transform", (FFT), that is to say the fast discrete Fourier Transform.
If the time sequence is made up of N samples of a real signal then the numbers of operations to be carried out for an FFT is the same as the number of computations which is performed by the FFT if the time sequence is formed by N complex samples. Because of the properties of real signals the number of operations which is performed in an FFT is excessively high if real signal samples are applied. As is described in reference 2 the number of operations at N real samples can be reduced to a number which is approximately equal to the number of operations which must be performed at N/2 complex samples.
This known arrangement is based on an FFT which is constructed in usual manner and which is exclusively suitable for processing complex signal samples and generating complex Fourier coefficients. By means of the preprocessing device and the first multiplying device the real signal samples are converted to complex numbers which are fed to the FFT.
If, as for signals having given symmetry properties, the Fourier coefficients are real the number of operations to be performed can be reduced still further, namely this number of operations can be reduced to approximately N/4 as compared with the number of operations in a conventional FFT (see ref. 3). To attain this reduction in the number of operations to be performed the conventional structure of the FFT is changed, which is undesirable or even impossible with a FFT computer unit which is intended as a module.